Oh, good call, didn't think to check that. Thief Badges appear to be drops on Blue Amity Beach and Fallen Bridge. The exact mechanics of drop rates aren't known, but in order to have a chance to get one you have to have your PCs in exactly 2 or 3 hexes (Beach) or all in 1 hex (Bridge) and then it's one of 6-7 items that you can get, 60% of the time. And then the item has to appear in your hex, which seems to happen more often than it "should" in my experience but no idea how much, and also we don't know the relative rate of items or how much the Item Scope and Lucky Bird help if you use those.
Still, even making some generous assumptions, if a player doesn't know how to get the Thief Badge (i.e. has the PCs finish in a random number of hexes) you're probably looking at a 3-5% chance at best of getting it on the beach, and lower on the bridge, per fight. That's in the range that I'm not opposed to the player hunting for a DL legal item this way (i.e. the Princess Saber has this rate on Fallen Bridge, and I'm okay with allowing that, although full disclosure that I lucked into it on my first playthrough and that probably colours my opinion) but too low for me to consider it against bosses.
